Some Theorems on Continua
نویسنده
چکیده
PROOF. Let {Gn} and {Hn} denote monotonie decreasing sequences of open sets which close down upon .Pi and F2 respectively. We may suppose that d and Hi are so chosen that G i # i = 0. Now, by Mullikin's theorem, there is a connected subset of C— C(Gw+27n) which has a limit point in Gn and a limit point in Hn. The closure of such a connected set is a subcontinuum of C which "extends" from Gn to Hn. If, then, we denote by Qn the set of all points of C — C' (Gn+Hn) which lie on subcontinua of C which extend (in the above indicated sense) from Gn to 13n, we have Qn^O.
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